{"id":"W2158578774","doi":"10.1142/s0219199705001787","title":"CONNECTIONS FOR GENERAL GROUP ACTIONS","year":2005,"lang":"en","type":"article","venue":"Communications in Contemporary Mathematics","topic":"Advanced Differential Geometry Research","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Connection (principal bundle); Group (periodic table); Group action; Pure mathematics; Curvature; Key (lock); Principal (computer security); Algebra over a field; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004411251,0.0006985588,0.0003443734,0.001462801,0.001095467,0.001347548,0.0004572732,0.000818169,0.006841684],"category_scores_gemma":[0.001273083,0.0002930075,0.0004162665,0.0008087961,0.002083167,0.003287859,0.001719104,0.001037442,0.0007150787],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007848633,"about_ca_system_score_gemma":0.0003494476,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006363356,"about_ca_topic_score_gemma":0.0006381913,"domain_scores_codex":[0.9996262,0.00006943184,0.00001636411,0.0001079504,0.000115456,0.00006461374],"domain_scores_gemma":[0.9995751,0.0000761342,0.00007843344,0.00007499625,0.0000733544,0.0001219635],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005388616,0.000003431438,0.0001685964,0.00001587574,0.000002855526,0.00008288155,0.0001337156,0.0008634565,0.0008076275,0.9950379,0.0004650851,0.002413092],"study_design_scores_gemma":[0.000004844935,0.0000166141,0.0004491697,0.00000998642,0.000004625464,0.0002046347,0.00006759086,0.004468787,0.0002666798,0.9859131,0.008586182,0.000007864195],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6054066,0.004352238,0.2077557,0.002282535,0.0006823511,0.0000996122,0.0004037495,0.0004585311,0.1785586],"genre_scores_gemma":[0.9678481,0.001093046,0.01277334,0.0002205783,0.0003431223,0.00004898485,0.0001711304,0.0000685165,0.01743327],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006841684,"threshold_uncertainty_score":0.02288771,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2263092964446952,"score_gpt":0.4267018019953899,"score_spread":0.2003925055506946,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}